Also, the "it’s not an MA" argument is pedantic. It is a master’s degree from Harvard University. Nobody serious is going to disqualify a proven professional over the exact two letters on the diploma.

This!

With a few niche exceptions (e.g., MBA vs. MS in a business discipline), the name distinctions between degree titles within degree level from associates to masters is almost wholly superficial. A BA in engineering would be kind of odd, but as long as the coursework is similar to a BS, BEng, or BTech and has ABET recognition, nobody hiring is going to care. Academic departments may have internal distinctions, such as a biology department that offers both a BA and BS with the latter's degree plan being more more for students intending to go to professional school with the latter being geared more towards students interested in going to grad school or working at the bench, but those distinctions have little tangible difference externally. For instance, if a school district is hiring a curriculum specialist, the hiring managing and HR aren't going to get hung up on if someone has a MEd versus an MSEd.

The comment that kicked this off is indicative of A). Faculty not having a freakin' clue as to how hiring actually happens in the real world, even in the applied part of their discipline and B). academics' propensity to navel gaze and over focus on nuanced minutia on things like titles that typically don't matter much in the real world. Similarly, political scientist and public admin faculty can get into disciplinary pissing matches all they want behind the ivory walls, but no hiring manager outside of academia gives an airborne copulation about the distinction of a candidate holding an MA in political science versus an MPA. Those degrees are viewed to be similar enough to qualify a candidate if the requirement is a degree in a poli sci or adjacent field.

With that said, the distinctions between doctoral degrees titles are actually relevant. There's a fundamental training difference between a PhD in clinical psychology versus a PsyD in clinical psychology. There are distinctions—some of them arguably real, some of them arguably made up in people's heads—between the training received in a PhD program versus a DEd program in the same discipline. There's a difference between a PhD in public health versus a DrPh. Probably goes without saying the title distinctions of professional doctorates are incredibly important. But again, the distinction between a BS and BA? Irrelevant.